When a monopolistic or extremely huge private company that deals in opinion and communication with the public does it, it may as well be the government, except you can’t vote them out of office, and boycotts are irrelevant.
Catering to the sensibilities of your paying customers is not censorship. They were paying this guy to entertain their paying customers. Instead he insulted them. NO surprise he lost his gig. But no one is preventing him from saying what he wants to say. Hereon he will just have to provide his own soap box.